Each shape has x, y, height, and width, but not when grouped. How do you make a group of shapes x, y, height, width?

Not sure I've understood. Anyway, when shapes are grouped, and you want to move one inside the group, double click on it. In The status bar at the bottom of the canvas should display "[nameofshape] in layer [nameofggroup]. Now input the new coordinates of the selected shape in the input box atop of the canvas, then deselect all. The object has moved inside the group, without ungrouping.

Hope this helps.